High-performance electrical system design requires the use of sophisticated interconnections between system components. These interconnections must be designed so as to achieve three interrelated objectives: minimize signaling delay between components; minimize electromagnetic cross talk noise between interconnections; and ensure immunity to external electromagnetic interferences. Two main examples of these interconnections are multiconductor transmission lines and connectors. The present invention is concerned mainly with multiconductor transmission lines.
Multiconductor transmission lines are present throughout any electrical system comprising several integrated circuits (chips). They are used on a printed circuit board (PCB) for signal transmission between different chipsets. Multiconductor transmission lines are also used to transfer signals inside a package containing the chip as well as to transfer signals inside the chip itself. PCB and package transmission lines are known in the art as off-chip transmission lines while the lines responsible for transferring signals within the chip are known in the art as on-chip transmission lines. The transmission line nature of an interconnection depends on the wavelength of the signal carried by the interconnection. With the constant increase in electronic system speed, the signal wavelengths are becoming shorter. The net result is that more and more of the interconnections are behaving as transmission lines, which makes the task of modeling and analyzing overwhelming. The situation is rendered even more complex by the fact that the on-chip and off-chip transmission lines behave very differently in terms of the losses (i.e., attenuation and the distortion) incurred by the signals they carry. Because of their small cross sections, on-chip transmission lines are very lossy relative to off-chip transmission lines. Among off-chip transmission lines, packaging transmission lines are in general more lossy than PCB transmission lines. These differences in location (on-chip, off-chip), length (short, long), losses (high, low), and signal wavelength make the efficient modeling, simulation, and analysis of transmission lines a difficult engineering task.
There are two main macromodeling approaches used to analyze the behavior of a transmission line. The first approach is based on a preliminary extraction of the pure delay (also called time-of-flight delay) incurred by the signal as it is transmitted. An instance of such approach is the method of characteristics (MoC) (Branin, IEEE Proc. Vol. 55, pp. 2012-2013, 1967) and its various generalizations (Gruodis and Chang, IBM J. of Res. Dev. Vol. 25, pp. 25-41, 1982). The second macromodeling approach represents the transmission line with a cascade of electrical cells, each cell comprising lumped circuit elements such as resistors, capacitors, and inductors. This approach is equivalent to approximating the transfer function of the transmission line, which is a transcendental function, with a rational (i.e., non transcendental) function (e.g. Dounavis et. al., IEEE Transaction on Advanced Packaging, Vol. 22, pp. 382-392, 2000). The first macromodeling approach is referred to as the delay extraction approach while the second macromodeling approach is referred to as the rational approximation approach.
It is well known in the art (e.g., Elfadel et. al., IEEE Transactions on Advanced Packaging, Vol. 25, pp. 143-153, 2002) that long, low-loss lines, such as coaxial cable (e.g., those connecting processing nodes in a supercomputer) are efficiently simulated using macromodels based on delay extraction approach. Short, high-loss transmission lines, such as on-chip bus lines (e.g., global bus connecting cable and CPU in a microprocessor) are efficiently simulated using macromodels based on rational approximation approach. Commercial circuit simulators, such as HSPICE, offer both types of modeling approaches to users. However, those simulators require the user to select which approach to use in a given situation. Users lacking expertise in transmission line theory may select the wrong or less efficient transmission line model (e.g., rational approximation model for a long, lossless line), thus incurring a significant cost in terms of transmission line simulation efficiency and accuracy. There is therefore a need to develop an automatic selection system and method for transmission line macromodels based solely on the physical and geometric characteristics of the transmission line. Such an automatic selection system can be part of a computer-aided-design (CAD) tool, such as a circuit simulator, that will handle all matters related to the efficient and accurate simulation of transmission lines throughout the electrical system. Such automatic selection will also be crucial for system-level simulation for high-performance electronic systems (e.g., mainframe computers) where the number of transmission lines is very large and it is not known a priori what type of macromodel is most appropriate for a given transmission line. The present invention satisfies these needs by providing a system and method for the automatic selection of transmission line macromodels.